Page 167 - A Course in Linear Algebra with Applications
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5.3: Operations with Subspaces 151
15. Find the dimension of the quotient space P n(R)/U where
U is the subspace of all real constant polynomials.
16. Let V be an n-dimensional vector space over an arbitrary
field. Prove that there exists a quotient space of V of each
dimension i where 0 < i < n.
17. Let V be a finite-dimensional vector space and let U and
W be two subspaces of V. Prove that
dim((C7 + W)/W) = dim(U/(U n W)).
